Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos

Details Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos

2007-08-06

arxiv.org/abs/0708.0755v3

Physics

Mathematical Physics

Notes from the lectures delivered at AGAQ conference (Istanbul, June 2006)

Scientific paper

In these notes we discuss the "self-reducibility property" of the Weil representation. We explain how to use this property to obtain sharp estimates of certain higher-dimensional exponential sums which originate from the theory of quantum chaos. As a result, we obtain the Hecke quantum unique ergodicity theorem for generic linear symplectomorphism $A$ of the torus $T^{2N}=R^{2N}/Z^{2N}.

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